Churn and Default
Introduction
Solar power is the fastest growing renewable energy source. Community solar projects lower the barrier to entry. This is accomplished by increasing the applicant pool by allowing those without rooftop access, such as renters or those in apartment buildings, and by lowering the financial burden of entry, as the fixed costs to install and operate the solar panels are collectivised rather than focused on one rooftop.
For potential customers, community solar contracts vary by their contract attributes. These include term length, cancellation fees, and potential savings rates relative to traditional utility bill companies. Given the importance of both the solar industry and the relatively incipient community solar industry, a dearth of research exists on how potential customer priorities are reflected in the likelihood of contract adoption.
This research seeks to fill this gap by developing quantitative measurements of community priorities in likelihood of contract adoption. An original data set comprised of potential community solar customers surveyed was collected. Along with respondents demographic information, draft contracts with varying degrees of contract attributes were shown to each participant and their contract adoption rates. Using a weighted logit model, the likelihood of contract adoption was analyzed by including predictors for various demographic data and contract attributes. Additionally, relative importance is through a multinomial logit model, allowing contract attributes and demographic information to be interpreted in predictive strength relative to respective reference groups.
Literature Review
to-do
Methods
This research focuses on community shared solar (CSS) programs that are third-party owned and have participants subscribe to ongoing payments. Typically, within these programs, customers are given predefined, discrete contract terms rather than being able to compare multiple offerings or select their own terms. Our research is attempting to mimic this approach by giving customers a randomly assigned contract and surveying them on their willingness to adopt this program.
Descriptive Statistics
| Variable | N | Percent | Variable | N | Percent |
|---|---|---|---|---|---|
| Sign Up | 2986 | Time Spent Reviewing Contracts | 2986 | ||
| … No | 1215 | 40.7% | … 01 Less review | 1202 | 40.3% |
| … Yes | 1771 | 59.3% | … 02 More review | 1784 | 59.7% |
| Contract Review Order | 2985 | Government Assistance | 2986 | ||
| … 01 First review | 1492 | 50% | … 01 None, Unknown, or Other | 1340 | 44.9% |
| … 02 Second review | 1493 | 50% | … 02 At least one gov’t program | 1646 | 55.1% |
| Savings Rate | 2986 | Race | 2986 | ||
| … 5% savings rate | 1001 | 33.5% | … 01 White | 1204 | 40.3% |
| … 10% savings rate | 1003 | 33.6% | … 02 Black | 580 | 19.4% |
| … 20% savings rate | 982 | 32.9% | … 03 Hispanic | 414 | 13.9% |
| Cancellation Fee | 2986 | … 04 Asian | 434 | 14.5% | |
| … 0 | 1495 | 50.1% | … 05 Other POC | 354 | 11.9% |
| … 250 | 1491 | 49.9% | Homeownership | 2986 | |
| Contract Length Pages | 2986 | … 01 Homeowner | 1728 | 57.9% | |
| … 10-page contract | 1491 | 49.9% | … 02 Renter | 1248 | 41.8% |
| … 20-page contract | 1495 | 50.1% | … 03 Other | 10 | 0.3% |
| Contract Length Years | 2986 | Income | 2986 | ||
| … 1-year contract | 1496 | 50.1% | … 01 High | 772 | 25.9% |
| … 25-year contract | 1490 | 49.9% | … 02 Moderate income | 1396 | 46.8% |
| Source | 2986 | … 03 Low income | 818 | 27.4% | |
| … 01 Qualtrics Panel | 2520 | 84.4% | Familiar with CS | 2986 | |
| … 02 Community | 466 | 15.6% | … 01 Less familiar | 1354 | 45.3% |
| … 02 More familiar | 1632 | 54.7% |
Demographic Comparison
| Race | Census_Total | Survey_Total | Weight |
|---|---|---|---|
| White | 52,150,851 | 602 | 86,629.32 |
| Hispanic or Latino | 24,830,970 | 207 | 119,956.38 |
| Asian | 9,585,168 | 217 | 44,171.28 |
| Black or African American | 9,540,566 | 290 | 32,898.50 |
| Other - POC | 3,841,546 | 177 | 21,703.65 |
| Total | 99,949,101 | 1,493 | 99,949,101.00 |
| Income | Census_Total | Survey_Total | Weight |
|---|---|---|---|
| 1: Less than 30% AMI | 10,158,670 | 218 | 46,599.40 |
| 2: Between 30-50% AMI | 8,281,900 | 191 | 43,360.73 |
| 3: Between 50-80% AMI | 10,865,560 | 360 | 30,182.11 |
| 4: Between 80-120% AMI | 12,901,840 | 338 | 38,171.12 |
| 5: More than 120% AMI | 29,350,940 | 386 | 76,038.71 |
| Total | 71,558,910 | 1,493 | 71,558,910.00 |
| x_hs | Census_Total | Survey_Total | Weight |
|---|---|---|---|
| 01 Homeowner | 21,679,273 | 864 | 25,091.75 |
| 02 Renter | 14,590,602 | 624 | 23,382.38 |
| Total | 36,269,875 | 1,488 | 108,399,374.72 |
Sources:
Race: 2020 5-Year ACS, Table B03002 Homeownership: 2020 5 Year ACS, Table B25003 Income: CHAS
Crosstab Graphics
Savings Rate & Income
Savings Rate & Race
Race & Income
Cancellation Fee & Income
Cancellation Fee & Race
Contract Years & Income
Contract Years & Race
Model
A number of independent variables will be used for both contract attributes and demographic data. Interaction variables will be tested for significant, along with a initial stepwise regression to determine which variables to initially include. The below equation is a summary of the full model used in this analysis. The dependent variable is a binary variable for contract adoption, \(y_{signup}\), where 1 signifies the contract was adopted and 0 signifies it was not.
\[\begin{equation} y_{signup} = \beta_{0} + \beta_{1}x_{sr} +\beta_{2}x_{cly} +\beta_{3}x_{clp} +\beta_{4}x_{cf} + \\ \beta{5}x_{inc}+\beta_{6}x_{race} + \beta{7}x_{hs} +\beta_{8}x_{fam} + \beta_{9}x_{rev} + \beta_{10}x_{ord}+ e_{i} \end{equation}\]
where,
- \(x_{sr}\): savings rates on monthly energy bill in contracts, listed at either 5%, 10% or 20%
- \(x_{cly}\): contract length years, either 1 or 25 years
- \(x_{clp}\): contract length pages, either 10 or 20 pages
- \(x_{cf}\): cancellation fee, either zero or $250
- \(x_{inc}\): income, listed as Low (up to 50% of AMI), Moderate (50% - 120% of AMI), or High (>120% AMI)
- \(x_{race}\): Categories include Asian, Black or African American, Hispanic or Latino, White and Other POC
- \(x_{hs}\): Homeowner status for Homeowner, Renter or Other
- \(x_{fam}\): More or less familiar with community solar
- \(x_{rev}\): How much respondent reviewed the contract; up to half the contract review is captured by “less review”, over half and up to the whole contract is “more review”
- \(x_{ord}\): Contract review order, likely not necessary.
Other variables of interest to consider: government program - x_govt
Results
Regression Tables
Table 1
##
## Regression Table 1
## ===========================================================================================
## Dependent variable:
## ------------------------------------------------------------------
## Sign Up
## (1) (2) (3) (4)
## -------------------------------------------------------------------------------------------
## Savings Rate 10% 0.125 0.126 0.126 0.127
## (0.090) (0.090) (0.090) (0.091)
##
## Savings Rate 20% 0.089 0.090 0.090 0.082
## (0.087) (0.087) (0.087) (0.087)
##
## Contract Length 25 Years -0.202*** -0.202*** -0.213***
## (0.076) (0.076) (0.076)
##
## Contract Length 20 Pages -0.046 -0.046 -0.053
## (0.072) (0.072) (0.073)
##
## Cancellation Fee 250 0.001 0.008
## (0.075) (0.075)
##
## High Income 0.210
## (0.137)
##
## Moderate Income 0.561***
## (0.120)
##
## Constant 0.304*** 0.426*** 0.425*** 0.118
## (0.073) (0.091) (0.097) (0.126)
##
## -------------------------------------------------------------------------------------------
## Observations 2,975 2,975 2,975 2,975
## R2 0.001 0.004 0.004 0.023
## chi2 1.964 (df = 2) 9.619** (df = 4) 9.619* (df = 5) 51.020*** (df = 7)
## ===========================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Table 2
##
## Regression Table 2
## ==========================================================================================================
## Dependent variable:
## ---------------------------------------------------------------------------------
## Sign Up
## (1) (2) (3) (4)
## ----------------------------------------------------------------------------------------------------------
## Savings Rate 10% 0.115 0.120 0.158* 0.159*
## (0.091) (0.091) (0.096) (0.096)
##
## Savings Rate 20% 0.077 0.078 0.117 0.120
## (0.088) (0.088) (0.094) (0.094)
##
## Contract Length 25 Years -0.209*** -0.223*** -0.229*** -0.226***
## (0.076) (0.077) (0.081) (0.081)
##
## Contract Length 20 Pages -0.065 -0.065 -0.067 -0.057
## (0.073) (0.073) (0.076) (0.076)
##
## Cancellation Fee 250 0.013 0.012 0.037 0.041
## (0.075) (0.076) (0.081) (0.081)
##
## High Income 0.290** 0.231 0.356** 0.348**
## (0.144) (0.146) (0.157) (0.158)
##
## Moderate Income 0.601*** 0.540*** 0.535*** 0.526***
## (0.122) (0.124) (0.132) (0.132)
##
## Black 0.075 0.162 0.089 0.073
## (0.146) (0.148) (0.156) (0.157)
##
## Hispanic 0.224 0.319** 0.169 0.160
## (0.153) (0.158) (0.169) (0.170)
##
## Asian -0.136 -0.072 -0.017 0.004
## (0.151) (0.154) (0.164) (0.164)
##
## Other 0.303* 0.376** 0.440** 0.442**
## (0.177) (0.179) (0.189) (0.190)
##
## Renter -0.327*** -0.092 -0.070
## (0.108) (0.116) (0.116)
##
## More Familiar 1.470*** 1.478***
## (0.110) (0.110)
##
## More Reviewed 0.256**
## (0.101)
##
## Constant 0.026 0.167 -0.738*** -0.905***
## (0.149) (0.157) (0.179) (0.189)
##
## ----------------------------------------------------------------------------------------------------------
## Observations 2,975 2,975 2,975 2,975
## R2 0.028 0.035 0.178 0.182
## chi2 62.852*** (df = 11) 79.180*** (df = 12) 421.368*** (df = 13) 430.983*** (df = 14)
## ==========================================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Odds Ratios
Table 1
##
## Odds Ratio, Table 1
## ===========================================================================================
## Dependent variable:
## ------------------------------------------------------------------
## Sign Up
## (1) (2) (3) (4)
## -------------------------------------------------------------------------------------------
## Savings Rate 10% 1.133 1.134 1.134 1.136
## (1.094) (1.094) (1.094) (1.095)
##
## Savings Rate 20% 1.093 1.095 1.095 1.085
## (1.091) (1.091) (1.091) (1.091)
##
## Contract Length 25 Years 0.817 0.817 0.808
## (1.079) (1.079) (1.079)
##
## Contract Length 20 Pages 0.955 0.955 0.949
## (1.075) (1.075) (1.076)
##
## Cancellation Fee 250 1.001 1.008
## (1.078) (1.078)
##
## High Income 1.234
## (1.147)
##
## Moderate Income 1.752
## (1.127)
##
## Constant 1.355 1.531 1.530 1.126
## (1.076) (1.096) (1.101) (1.134)
##
## -------------------------------------------------------------------------------------------
## Observations 2,975 2,975 2,975 2,975
## R2 0.001 0.004 0.004 0.023
## chi2 1.964 (df = 2) 9.619** (df = 4) 9.619* (df = 5) 51.020*** (df = 7)
## ===========================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Table 2
##
## Odds Ratio, Table 2
## ==========================================================================================================
## Dependent variable:
## ---------------------------------------------------------------------------------
## Sign Up
## (1) (2) (3) (4)
## ----------------------------------------------------------------------------------------------------------
## Savings Rate 10% 1.121 1.128 1.172 1.172
## (1.095) (1.096) (1.101) (1.101)
##
## Savings Rate 20% 1.080 1.081 1.124 1.127
## (1.092) (1.092) (1.098) (1.098)
##
## Contract Length 25 Years 0.812 0.800 0.795 0.798
## (1.079) (1.080) (1.085) (1.085)
##
## Contract Length 20 Pages 0.937 0.937 0.935 0.944
## (1.076) (1.076) (1.079) (1.079)
##
## Cancellation Fee 250 1.014 1.012 1.038 1.042
## (1.078) (1.078) (1.084) (1.084)
##
## High Income 1.336 1.260 1.427 1.416
## (1.155) (1.157) (1.170) (1.171)
##
## Moderate Income 1.825 1.716 1.708 1.692
## (1.129) (1.132) (1.141) (1.141)
##
## Black 1.078 1.176 1.094 1.076
## (1.157) (1.159) (1.169) (1.170)
##
## Hispanic 1.251 1.376 1.184 1.173
## (1.166) (1.171) (1.184) (1.185)
##
## Asian 0.873 0.931 0.983 1.004
## (1.163) (1.166) (1.179) (1.179)
##
## Other 1.354 1.456 1.553 1.556
## (1.193) (1.196) (1.209) (1.209)
##
## Renter 0.721 0.912 0.932
## (1.114) (1.123) (1.123)
##
## More Familiar 4.349*** 4.382***
## (1.116) (1.116)
##
## More Reviewed 1.292
## (1.106)
##
## Constant 1.026 1.182 0.478 0.404
## (1.160) (1.170) (1.196) (1.208)
##
## ----------------------------------------------------------------------------------------------------------
## Observations 2,975 2,975 2,975 2,975
## R2 0.028 0.035 0.178 0.182
## chi2 62.852*** (df = 11) 79.180*** (df = 12) 421.368*** (df = 13) 430.983*** (df = 14)
## ==========================================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Discussion
Main Takeaways
- Table 1
- Contract length of 25 years compared to 1 year remained a significant deterrent to contract acceptance rates.
- Relative to low income, moderate and higher income respondents were more likely to accept the contract, holding th effect of savings rate, cancellation fee, and contract length constant.
- Table 2
- Contract lenght remained a constant deterrance
- Homeowner status, rent vs homeowner, was not observed as a statistically significant effect on signup rate. Likely some multicollinearity due to effect (sign) varying from model 2 to model 4.
- After including familiarity and reviewed dummies, savings rate becomes statistically significant effect on likelihood of contract adoption.
- More familiar with community solar implies significantly more likely to adopt contract (suggests importance of education) - odds ratio of >4 in model 3 and 4
- In looking at contract adoption by race, Hispanics were the only group observed with a statistically significant effect in models 1 and 2. Relative to white, hispanic rates were higher. This effect is negated after additional IVs are introduces in models 3 and 4.
From Table 1, four models are presented analyzing changes in probability of sign up. Controlling for all other variables, contract length and income were found to have statistically significant effects on the rate of sign up. Contract length was found to have a strong negative impact on probability of contract adoption. For example, holding all variables constant, from model 2 we see that the odds ratio for contract length of 25 years is 0.782, meaning the group with contracts of 25 years are 0.782 times as likely as the group with contracts of 1 year of signing up, or a 21.8% decrease in odds of signing up.
Interestingly, lower income respondents were much less likely to adopt the contract, even when controlling for savings rate, contract length and number of pages, and cancellation fees. High income and medium income respondents were 1.3 and 1.7 times the odds to adopt the contract compared to low income respondents, controlling for contract attributes.
Secondary Analysis
The secondary analysis will include an ordered logit model to investigate the degree of which the same independent variables above influence the likert scale questions asked in the survey. Ordered logit models are commonly utilized with outputs of interest are categorized in discrete sequences, such as a Likert scale.
Would/Would Not Sign Up
Savings Rate
Tables 1-4 in output/regressions